Gap Reversal at Filling Factors $3+1/3$ and $3+1/5$: Towards Novel Topological Order in the Fractional Quantum Hall Regime

In the region of the second Landau level several theories predict fractional quantum Hall states with novel topological order. We report the opening of an energy gap at the filling factor $\nu =3+1/3$, firmly establishing the ground state as a fractional quantum Hall state. This and other odd-denominator states unexpectedly break particle-hole symmetry. Specifically, we find that the relative magnitudes of the energy gaps of the $\nu =3+1/3$ and $3+1/5$ states from the upper spin branch are reversed when compared to the $\nu =2+1/3$ and $2+1/5$ counterpart states in the lower spin branch. Our findings raise the possibility that at least one of the former states is of an unusual topological order.

Figure 1

Magnetoresistance traces in the second Landau level, i.e., in the filling factor range $2<\nu <4$, measured at $T=6.9\mathrm{mK}$. The region of the lower spin branch (LSB) and upper spin branch (USB) are clearly marked. Fractional quantum Hall states are marked by shaded stripes and their quantum numbers, while the reentrant integer quantum Hall states are indicated by shaded stripes only. Data in the LSB are from Ref. [33].

Figure 2

The magnetoresistance in USB SLL ($3<\nu <4$). Blue traces are measured at 6.9 mK, while the red one at 23.5 mK. Numbers mark various filling factors of interest. We note the absence of a FQHS at $\nu =3+2/3$, even though a local minimum is present in $R_{xx}$ at this filling factor. The dashed line is the classical Hall line and the star symbol is indicative of a developing RIQHS of a new type described in the text.

Figure 3

Arrhenius plots of the $R_{xx}$ minima at several odd-denominator filling factors in the LSB [panel (a)] and USB [panel (b)] of the SLL. Data at $\nu =2+1/3$ are from Ref. [33].